A wire of fixed length is wound on a solenoid of length and radius . Its Self Inductance is found to be . Now, if the same wire is wound on a solenoid of length and radius , then self inductance will be
Step 1: Given
Step 2: To find
We have to find the new inductance.
Step 3: Calculate the new inductance
Use the formula for self-inductance.
The expression for self-inductance is given by,
Where, is the magnetic permeability of free space, is the number of turns per unit length, is the area of the solenoid, and, is the length of the solenoid.
The area of a solenoid is given by,
Where, is the radius of the cross-section of the solenoid.
Substituting this value in equation (1).
Now, the length of the wire is given by,
Since the same wire is taken in both cases, then the circumference and number of turns will be the same for both wires.
Rearranging the above equation.
Now, substitute equation (3) in equation (2).
This will be the value of when the length of the wire is and radius is .
For, length and radius value of will be,
Thus, the self-inductance of the coil will be doubled.
Hence, the new self-inductance will be two times the original self-inductance.